Power and Power factor
- In a purely resistive AC circuit, the energy delivered by the source will be dissipated in the form of the heat by the resistance.
- In a purely capacitive or purely inductive circuit, all of the energy will be stored during one half of each cycle, and then returned to the source during the other half cycle – there will be no net conversion to heat.
- When there is both a resistive component and a reactive component, some energy will be stored, and some will be converted to heat during each cycle.
Power equations
Purely resistive circuit
Suppose a circuit with load
Instantaneous power dissipated by the load is given by:
Always:
Purely inductive circuit
Suppose a circuit with inductor
Instantaneous power dissipated by the load is given by:
Purely capacitive circuit
Suppose a circuit with inductor
Instantaneous power dissipated by the load is given by:
Power of a general load
Consider a general load with both resistive and reactive components. Depending
on how inductive or capacitive the reactive component, the phase shift between
voltage and current phasor lies between
Suppose the circuit is supplied a voltage of
This ends up with:
Average of over 1 cycle
Types of power
Reactive Power
Power delivered to/from a pure energy storage element is known as reactive power.
- Average power consumed by a pure energy storage element is zero.
- Current associated with it is not
. Transmission lines, transformers, fuses, etc. must all be designed to be capable of withstanding this current. - Loads with energy storage elements will draw large currents and require heavy duty wiring even though little average power is consumed.
- In all electrical and electronic systems, it is the true power (the resistive power) that does the work, the reactive power simply shuttles back and forth between the source and the load.
- This means that the apparent power supplied is a combination of the true and the reactive power.
Active power
Apparent power
The apparent power is essentially the effective power that the source “sees”
Power factor
In the above equation of
Power factor is:
- leading when
leads - lagging when
lags
Power triangle
- Take
phasor as the reference. - Draw
and phasors.